2 Answers
2

As soon as you put a bounty on a question the reputation is deducted from your total - as there are no refunds on bounties. As such the resulting "lower than posted" rep means they originally had around 800 rep prior to posting the bounty.

For example, my rep at the time of this comment is 1469. If I put a 500 rep bounty on a question, my rep would immediately decrease to 969, as per the reason @Marco described.
– Thomas Ward♦Jul 11 '11 at 18:16

No they can't offer more bounty then they currently hold but bounty is immediately subtracted when offered. If a user has 100 reputation and they offer a +50 bounty their rep immediately decreases to +50 reputation.